Question #279975

An inventor claims to have developed a heat


engine that receives 700 kJ of heat from a source


at 500 K and produces 300 kJ of net work while


rejecting the waste heat to a sink at 290 K. Is this


a reasonable claim? Why?

1
Expert's answer
2021-12-16T21:24:01-0500

Solution;

The maximum heat efficiency of the engine is the Carnot efficiency;

ηCarnot=1T2T1=1290500=0.42\eta_{Carnot}=1-\frac{T_2}{T_1}=1-\frac{290}{500}=0.42

Since efficiency is defined as;

η=workHeat\eta=\frac{work}{Heat}

0.42=W7000.42=\frac{W}{700}

W=294kJW=294kJ

Therefore it is impossible to have a work output greater than 294kJ and therefore the inventors claim is not reasonable.







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